You're on the right track. What's happening is that when you open something the way you have it uses 'EOF' as the record. 'EOF' is usually after the newline character so it will leave you with one '\n' each time through the loop, thus your pattern trying to match '\n\n' fails. You really don't need a regex at all, all you need to do is chomp. If you only have one newline on a particular line the line will be deleted because the '\n' character is all that's there. This should work:

while(defined($rivi = <ROWS>)) {
     chomp $rivi;
     ....
}
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Now chomp is removing all the '\n' characters so if you want each name on a separate line you'll need to add it back when you write to the file:

open(E,">>style1.txt") or die $!;
print E "$rivi\n"; # not understanding why you have $text here
close(E);
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That will append the $rivi and a newline. Unless you have some other info in $text that you defined before this block of code I don't think you really need it (if you want the output you showed above)

I can think of two other ways to do this, if you're interested in those please reply